Bounded Stochastic Perturbations May Induce Nongenetic Resistance to Antitumor Chemotherapy

2013 ◽  
pp. 171-187
Author(s):  
Alberto d’Onofrio ◽  
Alberto Gandolfi
Keyword(s):  
Stochastic Perturbations ◽  
Antitumor Chemotherapy

Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Ramalingam Sriraman ◽  
Rajendran Samidurai
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stochastic Perturbations ◽  
Practical Applications ◽  
Markovian Jump Parameters ◽  
Generalized Neural Networks ◽  
System Information ◽  
Dissipativity Analysis

Abstract This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

Randomly perturbed vibrations

1995 ◽  
Vol 32 (02) ◽  
pp. 417-428 ◽  
Author(s):  
M. Elshamy
Keyword(s):  
Dirichlet Boundary ◽  
Space Variable ◽  
Initial Conditions ◽  
Linear Wave ◽  
Stochastic Perturbations ◽  
Uniform Topology ◽  
Linear Wave Equation ◽  
Random Forcing ◽  
Continuity Properties ◽  
Positive Time

Let u ε(t, x) be the position at time t of a point x on a string, where the time variable t varies in an interval I: = [0, T], T is a fixed positive time, and the space variable x varies in an interval J. The string is performing forced vibrations and also under the influence of small stochastic perturbations of intensity ε. We consider two kinds of random perturbations, one in the form of initial white noise, and the other is a nonlinear random forcing which involves the formal derivative of a Brownian sheet. When J has finite endpoints, a Dirichlet boundary condition is imposed for the solutions of the resulting non-linear wave equation. Assuming that the initial conditions are of sufficient regularity, we analyze the deviations u ε(t, x) from u 0(t, x), the unperturbed position function, as the intensity of perturbation ε ↓ 0 in the uniform topology. We also discuss some continuity properties of the realization of the solutions u ε(t, x).

scholarly journals Extreme value theory for piecewise contracting maps with randomly applied stochastic perturbations

2016 ◽  
Vol 16 (03) ◽  
pp. 1660015 ◽  
Author(s):  
Davide Faranda ◽  
Jorge Milhazes Freitas ◽  
Pierre Guiraud ◽  
Sandro Vaienti
Keyword(s):  
Extreme Value Theory ◽  
Stationary Process ◽  
Higher Dimensions ◽  
Value Theory ◽  
Extreme Value ◽  
Extremal Index ◽  
Limiting Distributions ◽  
Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

Betulinic acid acetate, an antiproliferative natural product, suppresses client proteins of heat shock protein pathways through a CDC37-binding mechanism

RSC Advances ◽  
2016 ◽  
Vol 6 (48) ◽  
pp. 42537-42544
Author(s):  
Qi-Chao Bao ◽  
Lu Wang ◽  
Lei Wang ◽  
Xiao-Li Xu ◽  
Fen Jiang ◽  
...  
Keyword(s):  
Heat Shock ◽  
Heat Shock Protein ◽  
Natural Product ◽  
Betulinic Acid ◽  
Signaling Networks ◽  
Binding Mechanism ◽  
Oncogenic Signaling ◽  
Promising Target ◽  
Antitumor Chemotherapy ◽  
Client Proteins

CDC37 has emerged as a promising target in antitumor chemotherapy because of its significant role in oncogenic signaling networks.

scholarly journals Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

2012 ◽  
Vol 15 ◽  
pp. 71-83 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Evelyn Buckwar ◽  
Cónall Kelly ◽  
Alexandra Rodkina
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Equilibrium Solution ◽  
Test System ◽  
Dimensional System ◽  
Step Size ◽  
Stochastic Perturbations ◽  
Stability And Instability

AbstractWe perform an almost sure linear stability analysis of the θ-Maruyama method, selecting as our test equation a two-dimensional system of Itô differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the Itô formula in the context of an almost sure linear stability analysis.

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